I don't have a hardware wallet yet. Would I be wise to move my bitcoin out of Jaxx into another wallet, even though I do hold the private keys? I don't think they have added support for bitcoin cash yet.
Move them wherever you want, as long as you have exclusive control over the private keys of that wallet. It doesn't matter if you use a hardware wallet, Electrum, Jaxx, Bitcoin Core etc.
They don't necessarily need to add support for the other forks, you just have to import your private keys to the other forks' wallet software to claim them.